The investigation of plasma flows in filaments/prominences gives us clues to understanding their magnetic structures. We studied the patterns of flows in an intermediate prominence observed by Hinode/SOT. By examining a time series of Hα images and Ca II H images, we have found horizontal flows in the spine and vertical flows in the barb. Both of these flows have a characteristic speed of 10-20 km s?1. The horizontal flows displayed counterstreaming. Our detailed investigation revealed that most of the moving fragments in fact reversed direction at the end point of the spine near a footpoint close to the associated active region. These returning flows may be one possible explanation of the well-known counterstreaming flows in prominences. In contrast, we have found vertical flows?downward and upward?in the barb. Most of the horizontal flows in the spine seem to switch into vertical flows when they approach the barb, and vice versa. We propose that the net force resulting from a small deviation from magnetohydrostatic equilibrium, where magnetic fields are predominantly horizontal, may drive these patterns of flow. In the prominence studied here, the supposed magnetohydrostatic configuration is characterized by magnetic field lines sagging with angles of 13? and 39? in the spine and the barb, respectively.